Estimating primaries by sparse inversion of the 3D Curvelet transform and the L1-norm constraint

三维曲波变换LI范数约束稀疏反演一次波估计方法研究(英文)

In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination （SRME） method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equation- based method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.

本文将稀疏反演一次波估计(EPSI)方法进行了改进,使得EPSI转换成双凸LI范数约束的最优化问题,采用交替优化方式进行一次波反射系数和震源子波的交替估计,直接对一次波反射系数进行估计,可同时获得震源子波与一次波反射系数。在反演一次波反射系数时,将三维曲波变换引入进来作为稀疏约束,从而避免的SRME中的预测减去的过程。该方法不仅减少对有效信息的损伤,而且提高了多次波去除效果。该方法同样是基于波动方程的自由表面多次波压制技术,在复杂海底情况下具有良好的去除的效果。理论与实际数据试算取得良好效果。